2.2.1. Impact factor formula
Previous studies have identified climate change, generally yielding lower precipitation and increased temperatures, and local human activities, such as river water withdrawals and land use changes, as the two main factors leading to the altered run-off observations in the YRB (Cong et al., 2009). In the past half century, Yang et al. (2005) found warming temperatures at a rate of 1.28 °C/50 years and precipitation decreasing at a rate of 45.3 mm/50 years. As a relatively small sub-basin of the YRB, the Baimasi hydrological regime has also responded to these impacts for the past half century. To separate and quantify the influences of climate change and local human activities on the run-off variation, we have taken the 1960s as the baseline (benchmark) decade for this study. According to Cong et al. (2009), for the successive decades thereafter, i.e. 1970s, 1980s and 1990s, the run-off variation in response to climate change can be quantified by reconstructing the natural run-off from a hydrological model.
An analysis of observed run-off shows the combined impacts of lower precipitation and increased temperatures due to climate change and increased human activities such as direct river withdrawals. A hydrological model represents the non-linear transformation from precipitation to river run-off, and moreover, includes the influences of reduced precipitation and warmer temperatures due to a changing climate system. In this regard, the hydrological model is used to reconstruct the natural run-off, which is responsive to climate change. For this study, using the daily climatic data, we first calibrated the VIC hydrological model (Liang et al., 1994; Liang et al., 1996) to the baseline period of the 1960s as a benchmark. We then simulated the basin natural run-off for the subsequent three decades (1971–2000) with no consideration of local human activities on the sub-basin (i.e. land use change and artificial water intake). Therefore, the reconstructed run-off, hypothetically, is the result of hydrological response impacted by climate change (precipitation and temperature in this case) only, hereinafter Icc. Likewise, we define the run-off changes impacted by human activities as Iha. Thus, the difference between reconstructed natural run-off and observed run-off represents the hydrological response to Iha, which is the residual. The relative change in observed run-off (RO) since the 1960s can be attributed to the combined impacts of human activities and climate change (Iha + Icc):
where RO is the relative change in observed run-off over the 1960s baseline period (%), Iha indicates impact from human activities (%), Icc indicates impact from climate change (%), Ōbase is the observed mean decadal run-off for the 1960s baseline period (cubic metre per year) and Oi is the observed annual run-off (cubic metre per year) for the assessment period.
The relative change in reconstructed run-off over the baseline period (RC) can then be stated as:
where RC is the relative change in reconstructed run-off over the baseline period (%), Icc indicates the impact from climate change (%), R̄base is the reconstructed mean decadal run-off for the 1960s baseline period (cubic metre per year) and Ri is the reconstructed annual run-off for the assessment period (cubic metre per year).
RO includes impacts from both local human activities and climate change for the recent three decades as compared with the baseline decade of the 1960s, whereas RC is the relative change of reconstructed natural run-off caused by climate change factors only. From equations (1) and (2) we can separate the percentage of climate change impact Icc from the summation of combined impacts
Equation (3) calculates the proportional run-off change brought about by climate variation over observed run-off changes impacted by both climate and human activities. We therefore define pCC as the percentage of run-off change due to climate change as opposed to the total impact:
Likewise, pHA, the percentage of run-off change due to human activities, can be derived as:
Equations (1)–(5) constitute the IFF that quantitatively attributes separately the impacts of climate change and human activities on run-off in the study basin for the period 1950–2000. The next step is to reconstruct natural run-off, which is the run-off subject to climate change factors (i.e. temperature and precipitation) and not local human activities, using the VIC hydrological model given meteorological observations surrounding the basin (Figure 1).